Learning product graphs from multidomain signals

TL;DR

This paper introduces a method to learn the structure of product graphs from multidomain signals by estimating factor graph Laplacians, leveraging smoothness assumptions and convex optimization, demonstrated on synthetic and real air quality data.

Contribution

It proposes a novel convex optimization framework for learning factor graphs from multidomain data assuming a Cartesian product structure.

Findings

Explicit water-filling solution for noise-free data

Effective in synthetic and real air quality datasets

Framework handles complete and noise-free data efficiently

Abstract

In this paper, we focus on learning the underlying product graph structure from multidomain training data. We assume that the product graph is formed from a Cartesian graph product of two smaller factor graphs. We then pose the product graph learning problem as the factor graph Laplacian matrix estimation problem. To estimate the factor graph Laplacian matrices, we assume that the data is smooth with respect to the underlying product graph. When the training data is noise free or complete, learning factor graphs can be formulated as a convex optimization problem, which has an explicit solution based on the water-filling algorithm. The developed framework is illustrated using numerical experiments on synthetic data as well as real data related to air quality monitoring in India.